Trees with m-Matchings and the Third Minimal Hosoya Index

摘要

For a graph G, its Hosoya index is denned as the total number of independent edge sets of G. Hou in Discrete Appl. Math. 119(2002)251-257 characterized the trees with a given size of matching and having minimal and second minimal Hosoya index. In this paper, we determine the trees with m-matchings and the third minimal Hosoya index.